The Effect of Stress Redistribution in a Thick-Walled Sphere Made of Shape Memory Alloy at Direct Phase Transformation under Constant Pressure

A. A. Movchan; Мовчан А. А.; A. V. Sharunov; Шарунов А. В.

doi:10.31857/S0032823524020057

The Effect of Stress Redistribution in a Thick-Walled Sphere Made of Shape Memory Alloy at Direct Phase Transformation under Constant Pressure

Authors: Movchan A.A.¹, Sharunov A.V.²
Affiliations:
1. Institute of Applied Mechanics of the RAS
2. Moscow Aviation Institute
Issue: Vol 88, No 2 (2024)
Pages: 228-244
Section: Articles
URL: https://ruspoj.com/0032-8235/article/view/675065
DOI: https://doi.org/10.31857/S0032823524020057
EDN: https://elibrary.ru/XULYKA
ID: 675065

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Abstract

The coupled problems of changing the stress-strain and phase state in a thick-walled spherical shell made of a shape memory alloy, the material of which undergoes a direct thermoelastic phase transformation associated with a decrease in temperature uniformly distributed over the entire volume of the material under the action of constant internal or external pressure, are solved. The effects of significant overstressing of the body layers adjacent to the inner boundary and significant unloading of the layers adjacent to the outer boundary associated with the movement of the phase transition completion front through the material were found.

Keywords

shape memory alloys, thick-walled sphere, direct transformation, stress redistribution

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About the authors

A. A. Movchan

Institute of Applied Mechanics of the RAS

Author for correspondence.
Email: movchan47@mail.ru
Russian Federation, Moscow

A. V. Sharunov

Moscow Aviation Institute

Email: aleksej-sharunov@yandex.ru
Russian Federation, Moscow

References

Lihachev V.A., Kuz’min S.L., Kamenceva Z. P. Shape Memory Effect. Leningrad: Izd.-vo LGU, 1987. 216 p. (in Russian)
Lexcellent С. Shape-Memory Alloys Handbook. ISTE Ltd.; Wiley&Sons Inc., 2013. 379 р.
Lagoudas D. S. Shape Memory Alloys Modeling and Engineering Applications. Springer, 2008. 435 p. https://doi.org/10.1007/978-0-387-47685-8.
Kurdyumov G.V., Handros L. G. On thermoelastic equilibrium in martensitic transformation // Dokl. Phys., 1949, vol. 66, iss. 2, pp. 211–215. (in Russian)
Rabotnov Yu. N. Creep Problems in Structural Members. Moscow: Nauka, 1966. 752 p. (in Russian)
Rabotnov Yu. N. Introduction to Hereditary Mechanics of Solids. Moscow: Nauka, 1977. 384 p. (in Russian)
Rabotnov Yu.N., Papernik L. Kh., Stepanychev E. I. Application of nonlinear theory of heredity to the description of temporal effects in polimeric materials. // Polimer Mech., 1971, vol. 7, no. 1, pp. 63–73.
Dergunov N.N., Papernik L. Kh., Rabotnov Yu. N. Analysis of behavior of graphite on the basis of nonlinear heredity theory // J. Appl. Mech.&Tech. Phys., 1971, no. 1, pp. 235–240.
Rabotnov Yu. N. Suvorova J. V. The non-linear hereditary-type stress-strain relations for metals // Int. J. Solids&Struct., 1978, vol. 14, no. 3, pp. 173–185.
Materials with Shape Memory Effect: Vol. 2 / Ed. by Likhachev V. A. St. Petersburg: Izd-vo NIIH SPbGU, 1998. 374 p. (in Russian)
Lihachev V.A., Malinin V. G. Structural and Analytical Theory of Strength. St. Petersburg: Nauka, 1993. 471 p. (in Russian)
Rabotnov Yu. N. Mechanics of a Straining Solid. Moscow: Nauka, 1988. 712 p. (in Russian)
Volkov A.E., Kukhareva A. S. Calculation of the stress-strain state of a TiNi cylinder subjected to cooling under axial force and unloading // Bull. of the RAS: Physics, 2008, no. 11, pp. 1267–1270.
Volkov A.E., Kukhareva A. S. Calculation of the stress-strain state in an infinite shape memory alloy cylinder during cooling and heating at different speeds // Mech. Compos. Mater.&Const., 2009, vol. 15, no.1, pp. 128–136. (in Russian)
Volkov A. E. Microstructural modeling of alloy deformation under repeated martensitic transformations // Izv. RAS. Ser. Phys., 2002, vol. 66, no. 9, pp. 1290–1297. (in Rusian)
Movchan A. A. Coupling effects in bending problems for beams of a shape memory alloy // J. Appl. Mech.&Tech. Phys., 1998, vol. 39, no. 1, pp. 143–151.
Movchan A. A. Torsion of prismatic beams from shape memory alloys // Mech. of Solids, 2000, no. 6, pp. 119–128.
Movchan A. A. The Selection of the phase transition diagram approximation and model of disappearing of martensite crystals for shape memory alloys // J. Appl. Mech.&Tech. Phys., 1995, vol. 36, no. 2, pp. 300–306.
Raniecki B., Tanaka K., Ziolkowski A. Testing and modeling of NiTi SMA at complex stress state // Mater. Sci. Res. Int. Spec. Techn. Pub., 2001, vol. 2, pp. 327–334.
Lexcellent C., Vivet A., Bouvet C., Calloch S., Blanc P. Experimental and numerical determinations of the initial surface of phase transformation under biaxial loading in some polycrystalline shape-memory alloys // J. Mech.&Phys. Solids, 2002, vol. 50, pp. 2717–2735.
Volkov A.E., Emelyanova E. V., Evard M. E., Volkova N. A. An explanation of phase deformation tension-compression asymmetry of TiNi by means of microstructural modeling // J. Alloys&Comp., 2013, vol. 577, pp. 127–130.
Lomakin E.V., Rabotnov Yu.N. A theory of elasticity for an isotropic body with different moduli in tension and compression // Mech. of Solids, 1978, vol. 13, no. 6, pp. 825–831.
Cisse C., Zaki W., Zineb T. B. A review of constitutive models and modeling techniques for shape memory alloys // Int. J. Plasticity, 2016, vol. 76, pp. 244–284.
Gu X., Zhang W., Zaki W., Moumni Z. An extended thermomechanically coupled 3D rate-dependent model for pseudoelastic SMAs under cyclic loading // Smart Mater. Struct., 2017, vol. 26, art. no. 095047.
Tikhomirova K. Computation of phase and structural deformations in shape memory alloys. One-dimensional model // Mater. Today: Proc., 2017, no. 4, pp. 4626–4630.
Tihomirova K. A. Phenomenological modeling of phase and structural deformations in shape memory alloys. The one-dimensional case // Comput. Mech. Contin. Media, 2018, vol. 11, no. 1, pp. 36–50. (in Russian)
Movchan A.A., Movchan I. A., Sil’chenko L. G. Micromechanical model of non-linear deformation of shape memory alloys under phase and structure transformation // Mech. of Solids, 2010, vol. 45, no. 3, pp. 406–416.
Hachin V.N., Pushin V. G., Kondrat’ev V. V. Titanium Nickelide: Structure and Properties. Moscow: Nauka, 1992. 160 p. (in Russian)
Movchan A.A., Kazarina S. A., Sil’chenko A. L. Experimental identification of a nonlinear deformation model for a shape memory alloy during phase and structural transformations // Russ. Metall., 2019, no. 4, pp. 301–308.
Nushtaev D.V., Zhavoronok S. I. Dynamics of martensite phase transitions in shape memory beams under buckling and postbuckling conditions // IFAC Papers OnLine, 2018, vol. 51, no. 2, pp. 873–878.
Nushtaev D.V., Zhavoronok S. I. Abnormal buckling of thin-walled bodies with shape memory effects under thermally induced phase transitions // Adv. Struct. Mater., 2019, vol. 110, pp. 493–524.
Zhavoronok S. I. On the coupled model of the thermoelastic behavior of a shape memory alloy in intrinsic variables and some statement of buckling problems of shape memory elements // AIP Conf. Proc. Ser. “Int. Conf. of Comput. Meths. in Sci.&Engng. 2020”, 2021, pp. 120004. https://doi.org/10.1063/5.0047900
Movchan A. A. Method of analytical inverting of nonlinear constitutive relations of the combined model of phase and structural deformation of shape memory alloys // AIP Conf. Proc., 2022, vol. 2611, iss. 1, art. no. 100005. https://doi.org/10.1063/5.0120427
Movchan A. A. Phenomenological model of changes in phase-structural deformations in shape memory alloys // Mech. of Solids, 2020, vol. 55, no. 4, pp. 573–583.
Banderia E., Savi M., Monteiro P. Jr. Finite element analysis of shape memory alloy adaptive trusses with geometrical nonlinearities // Arch. Appl. Mech., 2006, vol. 76, pp. 133–144.
Alipour A., Kadkhodaei M., Ghaei A. Finite element simulation of shape memory alloy wires using a user material subroutine: Parametric study on heating rate, conductivity, and heat convection // J. Intell. Mater. Syst.&Struct., 2015, vol. 26, iss. 5, pp. 1–19.
Zolochevskij A.A., Bekker A. A. Introduction to ABAQUS. Har’kov: 2011. 49 p. (in Russian)